The total energy and electron addition and removal spectra
can,
in principle, be obtained exactly from the one-body Green’s
function (GF). In practice, the GF is obtained from an approximate
self-energy. In the framework of many-body perturbation theory, we
derive different expressions that are based on an approximate self-energy,
but that yield nevertheless, in principle, the exact exchange–correlation
contribution to the total energy for any interaction strength. Response
functions play a crucial role, which explains why, for example, ingredients
from time-dependent density functional theory can be used to build
these approximate self-energies. We show that the key requirement
for obtaining exact results is the consistent combination of ingredients.
Also when further approximations are made, as it is necessary in practice,
this consistency remains the key to obtain good results. All findings
are illustrated using the exactly solvable symmetric Hubbard dimer.